Variation in z

1 Intention

In this document, we are going to explore how diversity in species responses to one or both environmental variables, and different scenarios of correlation between them, may influence multifarious response diversity. Additionally, we are going to look at how different correlation between the environmental variables influence the calculated response diversity.

Within the project “response diversity in the context of multifarious environmental change”, we have been simulating species response curves using the Eppley performance curve.

With one environmental variable, the performance (i.e., rate) is given by:

• \(rate(E) = ae^{bE}(1 - (\frac{E - z}{w/2})^2)\)
• \(E\) is the values of the environmental factor.
• \(z\) controls location of maximum.
• \(w\) controls range of \(E\) over which the rate is positive.
• \(a\) scaling constant.
• \(b\) controls rate of increase towards the maximum rate, as \(E\) increases.

Adding a second environmental variable gives:

\(rate(E_1, E_2) = a_1e^{b_1E_1}(1 - (\frac{E_1 - z_1}{w_1/2})^2) + a_2e^{b_2E_2}(1 - (\frac{E_2 - z_2}{w_2/2})^2)\)

We now want to assess the role of diversity in response to one (or both) environmental variable(s), and investigate how different covariances in diversity of responses to E1 and E2 influence response diversity.

To do that, we are going to manipulate amount of diversity in responses to one or both env variables among the species, and also the correlation in the tolerances (position of optima, determine by the terms z1 and z2 in the above formula). We will make scenarios of communities with diversity in response to only E1, or both E1 and E2, with diversity in both that is positively correlated (co-tolerance) or negatively (anti-tolerance).

2 Variation in diversity in z1

2.1 High fluctuation in environmental change - negative correlation

Increasing variance in z1 - negative correlation between env variables (E1 and E2) with high fluctuations.

We now create 3 communities. Community 1 is characterized by low diversity in z1, community 2 has medium diversity in z1, and community 3 has high diversity in z1. z2 is constant in the 3 communities and fixed to a medium level of diversity.

E1 and E2 have high fluctuations and negative correlation.

Figure 2.1: Environmental variables with high variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

2.1.1 Community 1 - low diversity in z1.

(#fig:plotcomm1_neg)Community 1, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).

2.1.2 Community 2 - medium diversity in z1.

(#fig:plotcomm2_neg)Community 2, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).

2.1.3 Community 3 - high diversity in z1.

(#fig:plotcomm3_neg) Community 3, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).

2.1.4 Response diversity calculation

Figure 2.2: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

2.2 Low fluctuation in environmental change - negative correlation

Increasing variance in z1 - negative correlation between env variables (E1 and E2) with low fluctuations

We repeat the same steps as in the previous section, but this time E1 and E2 have a very small variance.

Figure 2.3: Environmental variables with low variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

2.2.1 Response diversity calculation

Figure 2.4: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

2.3 High fluctuation in environmental change - positive correlation

Increasing variance in z1 - positive correlation between env variables (E1 and E2) with high fluctuations

Same steps as before (3 communities with increasing diversity ib z1 while z2 is fixed), but the correlation between E1 and E1 is negative.

Figure 2.5: Environmental variables with high variation and positive correlation. (a) E1 changing over time. (b) E2 changing over time.

2.3.1 Response diversity calculation

Figure 2.6: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

2.4 Low fluctuation in environmental change - positive correlation

Increasing variance in z1 - positive correlation between env variables (E1 and E2) with low fluctuations

We repeat the same steps as in the previous section, but this time E1 and E2 have a very small variance.

Figure 2.7: Environmental variables with low variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

2.4.1 Response diversity calculation

Figure 2.8: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

2.5 High fluctuation in environmental change - no correlation

Increasing variance in z1 - no correlation between env variables (E1 and E2) with high fluctuations

Same steps as before (3 communities with increasing diversity in z1 while z2 is fixed), but there is no correlation between E1 and E1

Figure 2.9: Environmental variables with high variation and no correlation. (a) E1 changing over time. (b) E2 changing over time.

2.5.1 Response diversity calculation

Figure 2.10: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

2.6 Low fluctuation in environmental change - no correlation

Increasing variance in z1 - no correlation between env variables (E1 and E2) with low fluctuations

We repeat the same steps as in the previous section, but this time E1 and E2 have a very small variance.

Figure 2.11: Environmental variables with low variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

2.6.1 Response diversity calculation

Figure 2.12: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

2.7 Summary plot - Effects of z1 diversity and correlation between environmental variables on response diversity

Figure 2.13: Influence of the correlation between environmental variables and z1 diversity on response diversity. (a) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as dissimilarity (sign insensitive measure). (b) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as divergence (sign sensitive measure).

3 Variation in diversity in z1 and z2

Now we do the same, but having also z2 changing together with z1 with positive correlation. So, diversity in z1 and z2 are increasing gradually from low to high in the 3 communities (increasing co-tolerance scenario?).

3.1 High fluctuation in environmental change - negative correlation

Increasing variance in z1 and z2 - negative correlation between environmental variables (E1 and E2) with high fluctuations.

We now create 3 communities. Community 1 is characterized by low diversity in z1 and z2, community 2 has medium diversity in z1 and z2, and community 3 has high diversity in z1 and z2.

E1 and E2 have high fluctuations and negative correlation.

Figure 3.1: Environmental variables with high variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

3.1.1 Community 1 - low diversity in z1 and z2.

(#fig:plotcomm1.2_neg)Community 1, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).

3.1.2 Community 2 - medium diversity in z1 and z2.

(#fig:plotcomm2.1_neg)Community 2, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).

3.1.3 Community 3 - high diversity in z1 and z2.

(#fig:plotcomm3.2_neg)Community 3, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).

3.1.4 Response diversity calculation

Figure 3.2: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

3.2 Low fluctuation in environmental change - negative correlation

Increasing variance in z1 and z2 - negative correlation between env variables (E1 and E2) with low fluctuations.

We repeat the same steps as in the previous section, but this time E1 and E2 have a very small variance.

Figure 3.3: Environmental variables with low variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

3.2.1 Response diversity calculation

Figure 3.4: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

3.3 High fluctuation in environmental change - positive correlation

Increasing variance in z1 and z2 - positive correlation between env variables (E1 and E2) with high fluctuations

Same steps as before (3 communities with increasing diversity in z1 and z2), but there is positive correlation between E1 and E1

Figure 3.5: Environmental variables with high variation and positive correlation. (a) E1 changing over time. (b) E2 changing over time.

3.3.1 Response diversity calculation

Figure 3.6: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

3.4 Low fluctuation in environmental change - positive correlation

Increasing variance in z1 and z2 - positive correlation between env variables (E1 and E2) with low fluctuations

We repeat the same steps as in the previous section, but this time E1 and E2 have a very small variance.

Figure 3.7: Environmental variables with low variation and positive correlation. (a) E1 changing over time. (b) E2 changing over time.

3.4.1 Response diversity calculation

Figure 3.8: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

3.5 High fluctuation in environmental change - no correlation

Increasing variance in z1 and z2 - no correlation between env variables (E1 and E2) with high fluctuations

Same steps as before (3 communities with increasing diversity in z1 and z2), but there is no correlation between E1 and E1.

Figure 3.9: Environmental variables with high variation and no correlation. (a) E1 changing over time. (b) E2 changing over time.

3.5.1 Response diversity calculation

Figure 3.10: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

3.6 Low fluctuation in environmental change - no correlation

Increasing variance in z1 and z2 - no correlation between env variables (E1 and E2) with low fluctuations.

We repeat the same steps as in the previous section, but this time E1 and E2 have a very small variance.

Figure 3.11: Environmental variables with low variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

3.6.1 Response diversity calculation

Figure 3.12: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

3.7 Summary plot - Effects of z1 and z2 diversity and correlation between environmental variables on response diversity

Figure 3.13: Influence of the correlation between environmental variables and diversity in z1 and z2 on response diversity. In this scenario, diversity in z1 and z2 increases with positive correlation. (a) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as dissimilarity (sign insensitive measure). (b) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as divergence (sign sensitive measure).

4 Variation in diversity in z1 and z2

Now we do the same, but having also z2 changing together with z1 with negative correlation. So, diversity in z1 is increasing gradually from low to high in the 3 communities, while z2 decreases gradually in the 3 communities (anti-tolerance scenario?).

4.1 High fluctuation in environmental change - negative correlation

Increasing variance in z1 and z2 - negative correlation between env variables (E1 and E2) with high fluctuations.

We now create 3 communities. Community 1 is characterized by low diversity in z1 and high diversity in z2, community 2 has medium diversity in z1 and z2, and community 3 has high diversity in z1 and low in z2.

E1 and E2 have high fluctuations and negative correlation.

Figure 4.1: Environmental variables with high variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

4.1.1 Community 1 - low diversity in z1 and high diversity in z2.

(#fig:plotcomm1.3_neg)Community 1, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).

4.1.2 Community 2 - medium diversity in z1 and z2.

(#fig:plotcomm2.3_neg)Community 2, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).

4.1.3 Community 3 - high diversity in z1 and low in z2.

(#fig:plotcomm3.3_neg)Community 3, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).

4.1.4 Response diversity calculation

Figure 4.2: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

4.2 Low fluctuation in environmental change - negative correlation

Increasing variance in z1 and z2 - negative correlation between env variables (E1 and E2) with low fluctuations

We repeat the same steps as in the previous section, but this time E1 and E2 have a very small variance.

Figure 4.3: Environmental variables with low variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

4.2.1 Response diversity calculation

Figure 4.4: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

4.3 High fluctuation in environmental change - positive correlation

Increasing variance in z1 and decreasing in z2 - positive correlation between env variables (E1 and E2) with high fluctuations

Same steps as before (3 communities with increasing diversity in z1 and z2), but there is positive correlation between E1 and E1

Figure 4.5: Environmental variables with high variation and positive correlation. (a) E1 changing over time. (b) E2 changing over time.

4.3.1 Response diversity calculation

Figure 4.6: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

4.4 Low fluctuation in environmental change - positive correlation

Increasing variance in z1 and decreasing in 2 - positive correlation between env variables (E1 and E2) with low fluctuations.

We repeat the same steps as in the previous section, but this time E1 and E2 have a very small variance.

Figure 4.7: Environmental variables with low variation and positive correlation. (a) E1 changing over time. (b) E2 changing over time.

4.4.1 Response diversity calculation

Figure 4.8: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

4.5 High fluctuation in environmental change - no correlation

Increasing variance in z1 and decreasing in z2 - no correlation between env variables (E1 and E2) with high fluctuations

Same steps as before (3 communities with increasing diversity in z1 and z2), but there is no correlation between E1 and E1

Figure 4.9: Environmental variables with high variation and no correlation. (a) E1 changing over time. (b) E2 changing over time.

4.5.1 Response diversity calculation

Figure 4.10: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

4.6 Low fluctuation in environmental change - no correlation

Increasing variance in z1 and decreasing in z2 - no correlation between env variables (E1 and E2) with low fluctuations

We repeat the same steps as in the previous section, but this time E1 and E2 have a very small variance.

Figure 4.11: Environmental variables with low variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

4.6.1 Response diversity calculation

Figure 4.12: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

4.7 Summary plot - Effects of z1 and z2 diversity and correlation between environmental variables on response diversity

Figure 4.13: Influence of the correlation between environmental variables and diversity in z1 and z2 on response diversity. In this scenario, diversity in z1 increases with negative correlation with respect to diversity in z2. (a) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as dissimilarity (sign insensitive measure). (b) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as divergence (sign sensitive measure).

4.7.1 Focus on z2

Figure 4.14: Focusing on z2. (a) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as dissimilarity (sign insensitive measure). (b) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as divergence (sign sensitive measure).

5 Overall Summary plot - Effects of z1 and z2 diversity and correlation between environmental variables on response diversity

Figure 5.1: Influence of the correlation between environmental variables and diversity in z1 and z2 on response diversity. All data across all scenarios pooled together. (a), (b), and (c) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as dissimilarity (sign insensitive measure). (d), (e), and (f) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as divergence (sign sensitive measure).

6 Reducing mean z2

7 Variation in diversity in z1 and z2

Now we do the same, but having also z2 changing together with z1 with negative correlation. So, diversity in z1 is increasing gradually from low to high in the 3 communities, while z2 decreases gradually in the 3 communities (anti-tolerance scenario?).

7.1 High fluctuation in environmental change - negative correlation

Increasing variance in z1 and z2 - negative correlation between env variables (E1 and E2) with high fluctuations.

We now create 3 communities. Community 1 is characterized by low diversity in z1 and high diversity in z2, community 2 has medium diversity in z1 and z2, and community 3 has high diversity in z1 and low in z2.

E1 and E2 have high fluctuations and negative correlation.

Figure 7.1: Environmental variables with high variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

7.1.1 Community 1 - low diversity in z1 and high diversity in z2.

(#fig:plotcomm1.3_negz2)Community 1, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).

7.1.2 Community 2 - medium diversity in z1 and z2.

(#fig:plotcomm2.3_negz2)Community 2, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).

7.1.3 Community 3 - high diversity in z1 and low in z2.

(#fig:plotcomm3.3_negz2)Community 3, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).

7.1.4 Response diversity calculation

Figure 7.2: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

7.2 Low fluctuation in environmental change - negative correlation

Increasing variance in z1 and z2 - negative correlation between env variables (E1 and E2) with low fluctuations

We repeat the same steps as in the previous section, but this time E1 and E2 have a very small variance.

Figure 7.3: Environmental variables with low variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

7.2.1 Response diversity calculation

Figure 7.4: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

7.3 High fluctuation in environmental change - positive correlation

Increasing variance in z1 and decreasing in z2 - positive correlation between env variables (E1 and E2) with high fluctuations

Same steps as before (3 communities with increasing diversity in z1 and z2), but there is positive correlation between E1 and E1

Figure 7.5: Environmental variables with high variation and positive correlation. (a) E1 changing over time. (b) E2 changing over time.

7.3.1 Response diversity calculation

Figure 7.6: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

7.4 Low fluctuation in environmental change - positive correlation

Increasing variance in z1 and decreasing in 2 - positive correlation between env variables (E1 and E2) with low fluctuations.

We repeat the same steps as in the previous section, but this time E1 and E2 have a very small variance.

Figure 7.7: Environmental variables with low variation and positive correlation. (a) E1 changing over time. (b) E2 changing over time.

7.4.1 Response diversity calculation

Figure 7.8: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

7.5 High fluctuation in environmental change - no correlation

Increasing variance in z1 and decreasing in z2 - no correlation between env variables (E1 and E2) with high fluctuations

Same steps as before (3 communities with increasing diversity in z1 and z2), but there is no correlation between E1 and E1

Figure 7.9: Environmental variables with high variation and no correlation. (a) E1 changing over time. (b) E2 changing over time.

7.5.1 Response diversity calculation

Figure 7.10: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

7.6 Low fluctuation in environmental change - no correlation

Increasing variance in z1 and decreasing in z2 - no correlation between env variables (E1 and E2) with low fluctuations

We repeat the same steps as in the previous section, but this time E1 and E2 have a very small variance.

Figure 7.11: Environmental variables with low variation and negative correlation. (a) E1 changing over time. (b) E2 changing over time.

7.6.1 Response diversity calculation

Figure 7.12: Directional derivatives and response diversity for the three different communities. a, b, c. Species directional derivatives over time. d, e, f. Response diversity measured as similarity-based diversity metric. g, h, i. Response diversity measured as divergence (sign sensitive). Dashed lines indicate zero in panels a, b and c, and the median value of response diversity along the X-axis in panels d, e, f, g, h and i.

7.7 Summary plot - Effects of z1 and z2 diversity and correlation between environmental variables on response diversity

Figure 7.13: Influence of the correlation between environmental variables and diversity in z1 and z2 on response diversity. In this scenario, diversity in z1 increases with negative correlation with respect to diversity in z2. (a) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as dissimilarity (sign insensitive measure). (b) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as divergence (sign sensitive measure).

Figure 7.14: Focusing on z2. (a) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as dissimilarity (sign insensitive measure). (b) Effects of the correlation between environmental variables and z1 diversity on response diversity measured as divergence (sign sensitive measure).